Searching Chimeras in the Non Local Complex Ginzburg Landau Equation

In this work, we will study the existence of chimera states in the Complex Ginzburg-Landau (CGL) equation with a non-local interaction. We have studied analytically the stability of the plane wave solutions of the equation (coherent states) and, using that result and numerical simulations, we find that the transition between the turbulent phase (incoherence) and the plane wave phase (coherence) is supercritical. Therefore, chimeras, as states in which coherent and incoherent states coexist, can not form in the CGL with these conditions.

We have also changed the kernel of the interaction to a general kernel using a moment expansion. However, this has proved insufficient to produce the conditions for the existence of the chimeras. Further research can be made by adding other nonlinear terms to the CGL equation in order to generate the appropiate conditions to observe a coexisting region in parameter space between coherent and incoherent states.